
where \(\mathbf {\alpha }\)  denotes the hyper-parameters that specify the SF \(s_{\mathbf {\alpha }}\) ,
\(\mathcal {M}_{\text{val}}\)  refers to the validation performance (e.g., MRR on the validation set),
and \(\mathcal {L}_{\text{tr}}\)  refers to the training loss.
We use the self-adversarial negative sampling loss [1]},
which is defined as follows:
\(\begin{aligned}\mathcal {L}(\lbrace  {\mathbf {e}}, {\mathbf {r}}\rbrace ; s_{\mathbf {\alpha }})= - \log \ \sigma (\gamma -s_{\mathbf {\alpha }}(h,r,t))- \sum _{i=1}^{n} \frac{1}{k} \log \ \sigma (s_{\mathbf {\alpha }}(h^{\prime }_i,r,t^{\prime }_i)-\gamma ),\end{aligned}\) 
